STRATHAM, N.H. — New Hampshire, accustomed to its quadrennial turn in the national political eye, looked earlier this year like it might be in for a sleepy fall.

That’s no longer true.

The buzz about the New Hampshire Senate race intensified last week when a WMUR poll, which earlier this month showed Democratic Senator Jeanne Shaheen up 12 over her most prominent Republican challenger, former Massachusetts Republican senator Scott Brown, pegged the race as a statistical dead heat. Shaheen led by two points, 46 percent to 44 percent, within the margin of error.

That survey injected new energy into Brown’s campaign, which national Republican strategists have eyed warily, cognizant that the state has voted Democratic in the last three presidential elections.

That poll is an outlier in the race so far, but state and national political strategists from both parties have long said they expected the race to tighten. That is, in part, because of the vicissitudes of the political calendar and, in part, to New Hampshire’s proudly won reputation as a state beholden to neither political party.

And as national party strategists take notice, New Hampshire voters are being pummeled with political advertising in the race — both from the candidates themselves and from outside organizations. On Wednesday, for instance, Shaheen launched her first attack ad of the campaign, painting Brown as a pawn of big oil companies and a candidate looking out for himself, rather than the state. That same day, a super PAC called the Ending Spending Action Fund released a harshly negative ad accusing Shaheen of profiting personally from her time in the Senate.

Meanwhile, on the ground in New Hampshire, Brown has hammered Shaheen on her refusal to hold town halls, a time-honored Granite State political tradition. And he has, since entering the campaign, been working hard to tie her to Obama’s unpopular foreign policy decisions, first in the face of Russia’s expansionist maneuvers and now with the militant group the Islamic State (also known as ISIL).

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“Guess what?” Brown told a town hall meeting in Stratham. “I know you’ll be shocked to hear it, but he’s not up for re-election. But his number-one foot soldier is, Senator Shaheen.”

Shaheen aides say that, while the senator has not held town halls that meet the Brown campaign’s definition, she has consistently been sitting down with voters in open settings. Shaheen’s political brand in the state — she is a former governor, and her family has long been a political powerhouse there — is sturdy and has proved durable to political attacks, they insist.

Democratic strategists familiar with recent private polling say those surveys continue to give Shaheen a lead of up to seven percentage points.

On Thursday, hours before Obama addressed the issue from the White House press briefing room, Shaheen released a measured letter putting a small amount of distance between herself and the administration, urging Secretary of State John F. Kerry, whose 2004 presidential campaign she chaired, and Treasury Secretary Jack Lew to “do more to disrupt ISIL’s recruitment operations.”

But Shaheen repeatedly refused to say last week whether she would welcome Obama to New Hampshire to campaign for her.

By contrast, during a speech to the Rotary Club of Concord, Shaheen frequently mentioned the name of her fellow New Hampshire senator, Republican Kelly Ayotte.

And she cautiously navigated her response to a question about the federal health care law. Of patients forced to change doctors, she said, “That has not been a good aspect of the law.” But she declined to back the GOP effort to do away with the law.

“I don’t think repealing it is the answer,” Shaheen said.

Brown, too, faces challenges in how closely voters identify him with his own national party. The New Hampshire strain of Republicanism is starkly more centrist than the policies embraced by many of the GOP’s most visible figures across the country.

In that way, much of Brown and Shaheen’s fortunes in the final two months will depend on forces beyond their control. Strategists in both parties say their ability to move poll numbers could largely hinge on prevailing voter trends nationally. The issues of immigration and the Middle East, in particular, have the potential to drastically alter the race.

Obama is reportedly considering sweeping executive action on immigration policy. AFL-CIO president Richard Trumka on Thursday told reporters that a bold step on immigration could serve as a motivating factor for the party’s liberal base in this fall’s midterm elections.

The president is also under pressure to authorize airstrikes against ISIS, even as the nation has signaled its weariness after more than a decade of war. Congressional debate about that policy question could come in September, with Senate majority leader Harry Reid indicating that he hopes to bring a defense authorization bill to the floor next month.

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Those issues could change the contours of the race. And the recent poll showed that the campaign could veer in either direction. Nine percent of voters said they were unsure or did not know which way to vote.

“From the get-go, the Republican side of the equation has been trying to connect Jeanne Shaheen to Barack Obama, whether it’s the Affordable Care Act or anything else,” said Wayne Lesperance, a political science professor at New England College. “Anything like that can be used as a wedge issue, Republicans and the Scott Brown campaign will try to use.”

For Republicans, the prospect of a second Senate seat in New Hampshire is an almost too-good-to-be-true prize, and could help them amass the six seat flips they need this November to take back the Senate.

“This could be a seat that Republicans weren’t expecting to get, but could add to the overall math of taking the Senate,” Lesperance said.

Brown so far appears to have dealt effectively with his challengers in the Sept. 9 Republican primary, instead preferring to look ahead to November and engage Shaheen. Two of Brown’s fellow Republican candidates trail Shaheen by a significantly larger margin, according to the poll. Both former US senator Bob Smith and former state senator Jim Rubens lag Shaheen by 14 points. Shaheen is unopposed in her primary.